Adaptive lookup table: a graphical simulation component for recursively updating numeric data storage in table form

ABSTRACT

A system may include a memory to store a graphical block diagram model including a graphical block, the graphical block being associated with a lookup table and one or more inputs for receiving input data. The system may further include one or more processors to update data stored in the lookup table based on the received input data, where data stored in the lookup table includes data for simulating an embedded control system.

RELATED APPLICATIONS

This application is a continuation of Ser. No. 11/583,416, now U.S. Pat.No. 7,930,153, filed Oct. 18, 2006, which is a continuation of Ser. No.10/036,675, now U.S. Pat. No. 7,139,687, filed Dec. 31, 2001, all ofwhich are hereby incorporated by reference.

BACKGROUND

The invention relates generally to graphical block diagram modeling.

Dynamic systems may be modeled, simulated and analyzed on a computersystem using graphical block diagram modeling. Graphical block diagrammodeling graphically depicts mathematical relationships among a system'sinputs, states and outputs, typically for display on a graphical userinterface.

In a graphical block diagram model, graphical blocks describing thestatic or dynamic behavior of corresponding physical components aregraphically connected to each other in order to simulate the aggregatebehavior of the combined physical system or plant. The behavior of aphysical system, which may include mechanical or electronic components,can be described in terms of numeric data stored in table (matrix) ormulti-dimensional array format in computer memory. The resulting tableor array is referred to as a lookup table and is well known in the art.

In the simpler two-dimensional case, lookup tables correspond tomatrices studied in the field of mathematics. Each element of a matrixis a numerical quantity, which can be precisely located in terms of twoindexing variables. At higher dimensions, lookup tables are representedas a collection of matrices, whose elements are described in terms of acorresponding number of indexing variables. In the area of computerprogramming and simulation, lookup tables provide a means to capture thebehavior of a physical system. More specifically, the behavior of asystem with M inputs and N outputs can be approximately described byusing N M-dimensional lookup tables.

Lookup tables can be generated by experimentally collecting orartificially creating the input and output data of a system. In general,as many indexing parameters are required as the number of inputvariables. Each indexing parameter may range within a pre-determinednumber of values, which are called breakpoints. The set of allbreakpoints corresponding to an indexing variable is called a grid.Hence, a system with M inputs has M grids or sets of breakpoints. Forgiven input data, the breakpoints (in breakpoint sets corresponding tothe input variables) are used to locate the array elements where theoutput data of the system are stored. For a system with N output datavalues, N array elements are located and the corresponding data arestored at these locations in a computer memory.

In prior lookup table schemes, once a lookup table is created using thesystem input and output data, the corresponding multi-dimensional arrayof values can be used in applications without the need for regeneratingthe system output data. Only the input data is required to locate theappropriate array elements in the lookup table, and the approximatesystem output data can be read from these locations. Therefore, a lookuptable captures an input-output mapping of a static or dynamic system inthe form of numeric data stored at pre-determined array locations.

Prior graphical block-based modeling and simulation tools, e.g.,Simulink® from The MathWorks Inc, support graphical lookup table blocksthat provide for such a static mapping of input-output behavior of aphysical system. Because the behavior of actual physical systems canvary with time due to wear, environmental conditions, and manufacturingtolerances, however, the “static” lookup table block may not provide avalid representation of the plant characteristics at a given time.

SUMMARY

The present invention is therefore directed towards a graphical lookuptable block that takes into account the time-varying nature of thesystem behavior that it is used to describe. In particular, the presentinvention provides methods and systems for adapting the values of alookup table over time to account for additional data from the physicalplant or system that it models.

In one aspect, the invention provides methods and apparatus, includingcomputer program products, for table lookup. The methods includeproviding to a graphical block diagram model a graphical block thatdefines a lookup table and having inputs for receiving input data, andusing the graphical block to update content stored in the lookup tablebased on received input data.

Particular implementations of the invention may provide one or more ofthe following advantages.

Unlike prior static lookup table blocks, the adaptive lookup table blockof the present invention always provides a valid representation of plantdynamics even though plant behavior may be time varying. Moreover, theunderlying adaptation techniques of the adaptive lookup table block arerobust against reasonable measurement noise and provide appropriatefiltering of noisy output measurements.

The graphical block can be used in a simulation program to dynamicallyand efficiently update the data stored in a lookup table. That is, theblock forms part of a larger simulation model of a physical system,which is represented in a graphical simulation environment. Thisapproach is highly reusable and presents a flexible interface to a user.

The adaptive lookup table defined by the graphical block can be realizedin other forms, such as computer programs or code embedded inmicroprocessor hardware for real-time applications. Supplied in asuitable simulation environment as a graphical simulation block, themethod or methods defining the underlying lookup table of the block canbe used to automatically generate computer code for embeddedapplications.

Other features and advantages of the invention will be apparent from thefollowing detailed description and from the claims.

In one embodiment, a system may include a memory to store data definingto a graphical block diagram model including a graphical block, thegraphical block associated with one or more inputs for receiving inputdata and a lookup table for simulating a plant, the input data includingdata input to the plant and data output from the plant. The system mayalso include one or more processors to receive breakpoint data,partition the lookup table into cells based on the breakpoint data,initialize the lookup table with initial table data, update data storedin the lookup table based on the input data received at the one or moreinputs, adjust the breakpoint data to alter the number of cells in thetable, generate code to simulate the graphical block diagram model, andexecute the generated code.

In another embodiment, a computer-implemented method may includeproviding a graphical block in a graphical block diagram model, wherethe graphical block is associated with a lookup table and includes oneor more inputs for receiving input data. The method may further includeinitializing the lookup table with initial table data and updating datastored in the lookup table based on the received input data. Thecomputer-implemented method may also include generating code to simulatethe graphical block diagram model; and executing the generated code.

In a further embodiment, a computer-readable medium includinginstructions executable by at least one processor may include one ormore instructions for receiving, in a static operating mode, one or moreinput values for storing in a lookup table, determining at least onepreviously stored value corresponding to the input values, and producingoutput data using the at least one previously stored value. Thecomputer-readable medium may further include one or more instructionsfor receiving, in a dynamic operating mode, the at least one input valueand at least one additional value, and modifying the previously storedat least one value corresponding to the at least one input value basedon the at least one additional value. The computer readable medium mayalso include one or more instructions for receiving from a sensor the atleast one additional value. The computer-readable medium may alsoinclude one or more instructions for determining whether the sensor hasfailed and allowing for operation only in the static operating mode whenthe sensor has failed.

In an additional embodiment, an apparatus may include means forproviding a graphical block in a graphical block diagram model, wherethe graphical block is associated with a lookup table and inputs forreceiving input data. The apparatus may further include means forinitializing the lookup table with and breakpoint data and initial tabledata and means for updating data stored in the lookup table based on thereceived input data. The apparatus may also include means for generatingcode to simulate the graphical block diagram model; and means forexecuting the generated code.

DESCRIPTION OF DRAWINGS

FIG. 1 is a block diagram of an exemplary system simulation environmentin which processes of a graphical block diagram modeling/simulationmodule for graphical block diagram model development and execution, aswell as code generation, are executed.

FIG. 2 is an exemplary screen display from a GUI of a computer systemexecuting the model editor of the graphical block diagrammodeling/simulation module (of FIG. 1) during development of a graphicalblock diagram model that includes an adaptive lookup table block.

FIG. 3 is an exemplary block parameter dialog box in which a userspecifies block parameters for the adaptive lookup table block.

FIG. 4 is a block diagram of an adaptive table lookup corresponding tothe adaptive lookup table block shown in FIG. 2.

FIG. 5 is a depiction of an exemplary, two-dimensional cell-based(0^(th) order) adaptive table lookup.

FIG. 6 is a depiction of an exemplary, two-dimensional point-based(1.sup.st order) adaptive table lookup.

FIGS. 7A and 7B are exemplary plant surface plots generated usingmeasured data and using data produced by adaptive (cell-based) tablelookup, respectively.

Like reference numerals will be used to represent like elements.

DETAILED DESCRIPTION

Referring to FIG. 1, a system simulation environment 10 includes adynamic physical plant or system 12 having known input data 14 andmeasured output data 16. The output data 16 of the plant 12 can beproduced, for example, by placing sensors at appropriate locations in aplant 12. The input data 14 and the measured plant output data 16 areprovided to a data acquisition system 18. The data 14, 16 collected bythe data acquisition system 18 are made available to a computer system20 for analysis.

The computer system 20 is configured with a data acquisition application22 and graphical block diagram modeling and simulation module 24(hereinafter, simply, “the module”), both of which are implemented insoftware in memory 26. The data acquisition application 22 receives theexperimental data 14, 16 collected by the data acquisition system 18 andprovides that data to the module 24. The experimental data can beprovided to the application 22 in real-time over a network link or bus28 or, alternatively, can be stored in a disk file 30 for subsequentretrieval by the application 22 (as indicated by the dashed lines 32).Thus, the data acquisition system 18 need not be coupled to the system20 as shown.

The module 24 includes a model constructor/editor 34 and a blockslibrary 36, which includes, among other types of graphical simulationblocks, an adaptive lookup table block 38. The adaptive lookup tableblock 38 uses the input and output measurements of the plant behavior tocreate and update the contents of an underlying lookup table. Morespecifically, the block 38 uses the plant input data to locate table(array) elements by comparing the input data values with breakpointsdefined for each indexing variable, and uses the plant outputmeasurements to update the numeric values of the array elements. Thus,the block continuously improves the contents of the lookup table overtime. This continuous improvement of the table data is referred toherein as lookup table adaptation. The adaptation process involvescomplex statistical and signal processing algorithms to capture thetime-varying input-output behavior of the plant. The adaptive lookuptable block 38 will be described in further detail later.

Still referring to FIG. 1, the module 24 further includes a blockdiagram processing module (or engine) 40. The model editor 34, inconjunction with the library 36, is used by a user (of the computersystem 20) via a Graphical User Interface (GUI) 42 to construct anddisplay a graphical block diagram model which visually and pictoriallyrepresents aspects of a dynamic system of interest to that user. Theblock diagram processing engine 40 includes a compiler/linker 44 tointerpret the block diagram generated by the model editor 34, asimulator 46 that executes the interpreted block diagram to producesimulation results and a code generator 48 that converts the interpretedblock diagram to executable code (e.g., textual source code, such as C,or firmware source code for execution on an embedded processor), ortransmits signals that configure or can be used to configure a hardwaredevice, for example, a field programmable gate array. The simulationresults of the adaptive lookup table can also be presented to the useron the computer screen (as later shown in FIG. 7B).

In addition to the memory 24, the system 20 also includes a CPU 50 forexecuting the various components of the module 20, the GUI 42 and otherOS programs (not shown) for controlling system hardware. Although notshown, it will be understood that the system 20 can be, in otherrespects, of a conventional computer (e.g., PC, workstation) design andarchitecture. That is, the system 20 may include conventional system I/Operipherals, e.g., display, mouse, keyboard and the like, for enablinguser interaction with the system.

For illustrative purposes, the module 24 will be described within thecontext of a simulation environment that is based on the use of suchtools as MATLAB®, Simulink® and Real-Time Workshop®. All of theaforementioned tools are commercial software products available from TheMath Works, Inc. In addition, the data acquisition application 22 andsystem 18 may be implemented with the Data Acquisition Toolbox® and thexPC Target®, also available from The Math Works, Inc. The Simulink®software package includes a number of different tools, such as specialuser interfaces and navigational tools, e.g., a library browser, whichwill be referenced in the description to follow. Further details ofthese tools and interfaces can be had with reference to availableproduct documentation. It will be understood, however, that othergraphical block diagram based modeling software platforms could be used.

The module 24 enables users to copy graphical blocks into their modelsfrom the library 36 (or, optionally, from external libraries). Thus, auser operating the computer system 20 uses the blocks, for example, theadaptive lookup table block 38, to build a graphical block diagram usingthe model editor 34. A user selects blocks using a menu provided by theSimulink® library browser. Having opened a model window for a model tobe generated and/or edited, the user copies the selected blocks from thelibrary window to the model window, e.g., by selecting (“clicking on”) acorresponding library node or icon, dragging the block from the librarybrowser and dropping it in the model window.

The term “graphical block diagram” refers to a set of graphical blocks(or nodes) and a set of lines (or signals) that carry data between thegraphical blocks. Each graphical block typically performs a function andthat function (or equation) is a sub-component of an overall set ofequations describing a dynamic system. The function may be mathematicalin nature or it may be an operation such as reading data from a hardwaredevice. The graphical blocks may be parameterized with user-definedvalues, as will be described.

Using the functions or equations defined by each of the blocks, thegraphical block diagrams can be executed to produce simulation resultsand generate textual software or firmware source code automatically asdefined by the graphical blocks and signals in a model. Each of theequations is defined in a corresponding method (code module). Forexample, an output method, when invoked by the simulator 46 during modelexecution, determines an output signal based on a given input signal andblock parameter value(s).

The adaptive lookup table block 38 implements an array of table elementsand maps the table elements to one or more sets of indexed values or“breakpoints”, typically non-repeating, monotonically increasing values.The breakpoints are the values at which the relationship which the tablehas sampled is evaluated for a given index. The breakpoints defineintervals or segments in which the input value(s) may fall. The blocksdetermine the location of the input value relative to one of theintervals and use that location to locate the elements and theircorresponding numeric table data values. The input values that falloutside these intervals are handled as well. They may be ignored orprocessed by the adaptive lookup table 38, e.g., treated as if fallingwithin an end interval.

The breakpoints of a lookup table serve to partition the table inputspace into regions referred to as “cells”. Each cell, which can bemulti-dimensional, is delimited by two breakpoints for each indexingvariable.

In one form of table lookup, the values of the table are associated withrespective cells in the table. Thus, for example, a two dimensionaltable might have a cell that corresponds to the intervals (4, 5) for afirst variable x₁, and (7, 8) for a second variable x₂. In such a table,input values within those ranges (e.g., x₁=4.2 and x₂=7.5) would resultin the value of that cell being generated as the output of the lookuptable. This type of table lookup is referred to as cell-based lookup.

In another form of table lookup, the values stored in the lookup tableare associated with specific intersections of input variables. Forexample, in a two-dimensional table, a specific value might beassociated with the input values of x₁=4 and x₂=7, and a different valuemight be associated with the point at which x₁=4 and x₂=8, at which x₁=5and x₂=7, and at which x₁=5 and x₂=8. In such a table, output values forinput values that fall between such defined points (i.e. x₁=4.2 andx₂=7.5) may be generated by interpolation of the values associated withthe specific points that surround the given point. This type of tablelookup is referred to as a point-based lookup.

In one embodiment, the table lookup is a cell-based table lookup and theadaptation uses a cell-based table lookup. In the cell-based adaptation,the plant output data that is generated for given plant input data usedto update a cell value for the particular cell determined by the tablelookup for that input data directly, and that adapted cell value isprovided at the block's output. In a second embodiment, the table lookupis point-based and the adaptation uses a point-based table lookup. Inthe case of the point-based adaptation, the plant output data is used toupdate the values of the grid points around that cell, and these adaptedpoints (values) are then used to interpolate the exact point at theposition identified by the plant input data. The interpolated point isprovided at the block's output. Both of these embodiments will bedescribed in further detail below.

The adaptive lookup table block 38 presents one abstraction of a lookuptable generation and adaptation process to a high-level user interface.The adaptive lookup table block 38 can be inserted into a physicalsystem model in a graphical simulation environment and provides thenecessary connectivity with other simulation blocks in the overallmodel. Once the user places the graphical simulation block into thelarger simulation model, the inputs and outputs of this component can beconnected with other components in the model.

FIG. 2 illustrates a Simulink® model window 60 that displays anexemplary block diagram model 62 created by a user using the modeleditor 34 and employing the adaptive lookup table block 38. The adaptivelookup table block 38 is usable to create multi-dimensional lookuptables from empirically gathered physical plant or system data.

In the illustrated embodiment, the block 38 receives the plant data,including plant input data “x” 64 and plant output data “d” 66 asinputs. The plant input data are coupled to respective input data ports68, which receive the plant input data from the external data collectionhardware via the data acquisition application 22. The plant output data“d” 66 is received from other ports not shown in this diagram, andultimately from the output of the plant. The plant input data 64 arecoordinate data and the plant output data 66 are system outputmeasurements, and therefore correspond to the input data 14 and outputdata 16 (from FIG. 1), respectively. For example, if the plant 12represents an engine and a user wishes to create a lookup table to modelbehavior of the engine's efficiency as a function of engine RPM andmanifold pressure, then the plant input data values x₁ and x₂ wouldcorrespond to values of RPM and manifold pressure, respectively, and thevalue of plant output data “d” would correspond to the measured valuefor efficiency. In the example model 62, the block 38 is configured toperform a two-dimensional lookup table, but can be configured toaccommodate any number of inputs “x” 64. More generally, it will beappreciated that an application of the adaptive lookup block 38 need notbe limited to the implementation shown in FIG. 2.

In addition, the block inputs can include various control signals, suchas an adaptation enable/disable input 70 and a locking enable/disableinput 72. The adaptation enable/disable input 70 is used to enable ordisable the adaptation process. Thus, the user has the ability to start,stop or reset the lookup table adaptation through the use of theadaptation enable/disable input 70. If the lookup table adaptationfunctionality is disabled, then the table lookup becomes a static tablelookup. It may be desirable to disable the adaptation in this manner if,for example, the user notices that there is little change in the valuesof the output data over time. The state of the input 70 is determined bythe setting of switch logic 74 to which the input 70 is connected. Thelocking enable/disable input 72 is used to restrict the adaptationprocess to particular elements of the lookup table. More specifically,the lock input 72, in conjunction with other logic, e.g., logic 75,allow the user to update only a particular cell when the plant inputdata would otherwise place the updating activity outside of that cellduring a table lookup/adaptation operation.

The outputs of the adaptive lookup table block include a currentlyadapted table output value “y” 76, an index number of the currentlyadapted lookup table cell (i.e., cell number 78), or indices of pointsaround the cell, and, if required, post-adaptation table data “T” 80.The table data output 80 may be useful for viewing the table contents inthe model window or generating surface plots, as shown in FIG. 7B.

The cell number 78 can be used for different purposes. For example, andas shown in the figure, it can be used to maintain an index of maturityblock 82. The index of maturity block 82 counts how many plant outputdata points the table has received within a particular cell. Thus, theindex of maturity block 82 tells the user something about the precisionof the table values: the more points within a table cell, the moreprecise is the adapted value for that cell. The cell number can also beused to track which points in the table are being adapted. If a specifictest is designed to generate data in a special order, then the cellnumber could be compared with the expected order to ensure that thatspecial order is followed.

Referring back to FIG. 1, the library 36 is a repository of classes thatcorrespond to the blocks. When a graphical class is used in a model, itis said to be instantiated, i.e., an instance of the graphical class iscreated for use in the model. Such an instance is a link to thegraphical class that resides in the library 36. The behavior of a blockin a block library may be defined in terms of parameters that the usermay specify when creating an instance of the block. The behavior of theblock is akin to the behavior of a template class as used in objectoriented programming languages such as C++. Block parameters are classmembers that are specified when a user constructs a new instance of aclass. Instances associated with the class have parameter specificationinterfaces that allow a user to set values for these block parameters.On the user's GUI, such as the GUI 42 (of FIG. 1), such parameterspecification interfaces take the form of a dialog box with variousparameter fields (as will be described with reference to FIG. 3, below).Thus, the user supplies the block parameters to the block method for theappropriate block through a dialog box associated with the block.Alternatively, the user can specify parameter values programmaticallyusing a textual API (e.g., the Simulink® ‘set_param’ command). Thus,each block in the block diagram model 62 can have parameters that arespecified by a user for use in the block methods for those blocks.

FIG. 3 shows a parameters dialog box 90 for the adaptive lookup table38. The dialog parameters that can be specified for the adaptive lookuptable 38 can include the following: number of table dimensions 92;initialization data, including one set of breakpoints for each indexingvariable 94, initial lookup table data 96; and a user-defined elementindexing scheme (e.g., cell numbering matrix) 98. It is also possible tospecify a table name 100; adaptation method 102; and adaptation speed104. Also, and as is shown in the exemplary GUI dialog box 90, it ispossible to specify the inputs and outputs to be used during simulation.For example, the dialog box 90 allows the user to select any of thefollowing: use of one input port as initial table data port 106; use ofa table data (matrix) output port 108; use of the adaptationenable/disable port 110; and use of the cell lock enable-disable port112. Thus, it can be appreciated that most of the adaptive lookup tableinput and output ports, such as the enable and lock signals, and thetable data output, for example, are user-configurable and can be turnedon or off via the dialog box 90.

In the embodiment depicted in FIGS. 1 and 2, the plant output data maycome from sensor measurements collected by running various tests on theplant 12, and the measured data (along with the corresponding plantinput data) is provided to the adaptive table block 38 togenerate/maintain the lookup table describing the relation between thesystem inputs 14 and output 16. When the model 62 is executed duringsimulation, the initial table begins to adapt to new plant data inputs.Copied to the table output y 76 is the value of the particular arrayelement currently being updated 76 (cell-based) or value interpolatedfrom the array elements being updated (point-based), the index number 80representing the position of the adapted element(s) in the lookup tableaccording to a user-defined numbering scheme (e.g., cell number), and,possibly, the adapted lookup table data 80 in its entirety.

Once the table is set up and initialized (via the user-specified blockparameter values), the execution of the model during simulation causesadaptation algorithms defined for the block to begin learning theunknown values of the lookup table elements. These algorithms use theinput and output measurements of the plant behavior to dynamicallycreate and update the contents of the lookup table. Eventually, after asufficient number of input values has been received so as to populate asufficient number of cells or points in the table with stable values, auser may choose to disable the adaptation process and utilize the tableas a static table for modeling the physical plant. Thus, in theembodiment described thus far, the simulation process serves to capturea model of the plant in the form of a lookup table.

Alternatively, although not shown, the block 38 could be used in a modelof a plant having an adaptive lookup table as part of its functionality.That is, rather than receiving data from a physical plant or system, theadaptive lookup table could receive data from other functional blocks ina block diagram model. In this latter scenario, the simulator 46, inexecuting the block diagram model, would simulate the behavior of theoverall system, including the adaptive lookup table (as graphicallyrepresented by the block 38). In such an application, the block's inputswould be fed by other functional component blocks in the model, that is,the inputs would receive simulated plant data, and thus the computersystem 20 would not require use of internal or external plant dataacquisition software or hardware (as was depicted in FIG. 1).

In general, the adaptive lookup table 38 operates as follows. When theadaptation mechanism is disabled, the lookup table acts as a standardstatic lookup table, providing table output values y 76 in response toreceived plant input values x 64. When the adaptation mechanism isenabled, the lookup table takes the following steps. It receives theplant input values x 64 and plant output value d 66. It then determineswhat, if any, stored values already in the table would be relevant fordetermining the table output value y 76 corresponding to the plant inputvalues x 64. In other words, in the cell-based embodiment, it determinesthe value of the cell corresponding to plant input values x 64, whereasin the point-based embodiment, it determines the values of pointsimmediately surrounding the point defined by input values x 64. It thenuses the plant output data d 66 to modify the existing relevant value(s)in the table. Finally, it generates an output based on the newly updatedtables value(s), which is provided on table output y 76.

Various techniques may be utilized to modify existing table values usingplant output data d 66. A simple method would be to simply replace theexisting values with the newly received plant output data d 66. Howeversuch a technique would, under some conditions, create inaccuracies dueto noise on the input. Therefore, as input values 64 and output values66 are received by adaptive lookup table 38, it is desirable that thetable respond in a robust and noise tolerant way, while rapidly adaptingto changing output values. Thus, the adaptation algorithms utilizevarious statistical and signal processing methods for robust, noisetolerant, and fast adaptation of the lookup table data. Since thesimulation block 38 and the GUI dialog 90 provide a high-level interfaceto user inputs and encapsulate the statistical computations, the complexdecision and adaptation mechanisms may be transparent to the user. Thedetails of these mechanisms will now be described in some detail.

Referring to FIG. 4, a lookup table generation and adaptation process120 defined for the graphical block 38 is shown. In the figure, smallletters denote numbers (e.g., d(n)), bold small letters denote vectors(e.g., x(n)), capital letters denote sets (e.g., P(n)), and capital boldletters denote multi-dimensional tensors (or arrays) (e.g., T(n)). Inthe embodiment shown, the process 120 includes four functionalcomponents: indexing logic 122, table numbering 124, adaptationalgorithm 126 and table data processing 128. The indexing logic 122receives as inputs the breakpoints 94, the lock signal 72 (optionally)and the input data 64, represented here as an input vector at time n,“x(n)”. For a number of plant inputs “l”, the input vector isx(n)=[x₁(n), . . . , x_(l)(n)]^(T). For x(n), the corresponding plantoutput 66 (either measured or simulated, as discussed above), alsorepresented as a vector at time n, is “d(n)”. The plant output d(n) 66is provided to the adaptation algorithm 126.

The indexing logic 122 uses x(n) 64, breakpoints 94 and lock signal 72(if used) to generate indices P(n) 130. The indices 130 are provided tothe table numbering 124 and the table data processing 128. The tablenumbering 124, which also receives the table cell numbers 98 (from theuser block parameter dialog input), uses the cell numbers 98 and theindices 130 to select from the cell numbers 98 the cell numbercorresponding to the indices 130. The table data processing 128 receivesthe initial table data 96 (from the user block parameter dialog input),and uses the indices 130 to determine an element or elements at thecorresponding table cell location. That element is the element to beupdated to take into account the new data, that is, d(n). Thus, thetable processing 128 provides the currently stored element or elements132 to the adaptation algorithm 126, which adapts each element valueaccording to a particular algorithm, as will be described below, andreturns the adapted value of that element or elements to the table dataprocessing 128. The table data processing 128 stores the adapted value.The table data processing 128 provides an adapted plant output value asthe table output 76, represented as output y(n) at time n. In thecell-based embodiment, y(n) is the same as the stored adapted value,that is, the adapted cell value. In the point-based embodiment, once theelement (grid point) values are adapted, an interpolation is performedusing the adapted points to determine the adapted output value y(n). Ifthe table data output 80 is configured by the user, then the table dataprocessing 128 also provides as an output the table data 80, or T(n),which incorporates the results of the current adaptation iteration.

For each plant input, x_(i), there is a corresponding vector ofbreakpoints b_(i) with k_(i) elements, which grids the input space inthe i^(th) dimension. The set of all breakpoints which grid thel-dimensional input space is given byB={b _(i)εR^(k) ^(i) └k _(i) εN,i=1, . . . ,},  (1)where each b_(i)=[b_(i)(1), . . . , b_(i)(k_(i))]^(T).

Given the input vector x(n), the set of indices, P(n), is determined sothat each index within the set locates the input value x_(i)(n) withinthe corresponding vector of breakpoints, b_(i). That is,P(n)={p _(i)(n)εN|b _(i)(p _(i))≦x _(i)(n)≦b _(i)(p _(i)+1),i=1, . . .,l}.  (2)The vector of indices p(n) is obtained by ordering the set P(n):p(n)=[p _(l)(n), . . . ,p _(ζ)(n)]^(T).  (3)The corresponding set of fractions and the vector of fractions are givenbyF(n)={f _(i)(n)εR|x _(i)(n)=(1−f _(i)(n))b _(i)(p _(i))+f _(i)(n)b_(i)(p _(i)+1),i=1, . . . ,l}.  (4)andf(n)=[f ₁(n), . . . ,f _(l)(n)]^(T).  (5)The set of indices P(n) corresponding to an input x(n) at time n is usedto select m elements of the current table data T(n):W(n)={w _(j)(n)εR|w _(j)(n)=w _(j)(n;P(n)),j=1, . . . ,m},  (6)where the number m depends on the type of adaptation scheme that isused. The set W(n) contains those elements of the table T(n) that willbe adapted in the current iteration. The ordered set of elements of W(n)is represented by the vector w(n):w(n)=[w _(l)(n), . . . ,w _(m)(n)]^(T).  (7)

The adaptation scheme uses the vector w(n) and the plant output d(n) togenerate the table output, y(n), an estimation error e(n) and the newtable element values w(n+1):y(n)=w ^(H)(n)u(n)  (8)e(n)=(d(n)−y(n)  (9)w(n+1)=w(n)+h(w(n),e(n),u(n)),  (10)where the form of the vector u(n), and the vector function h( ) dependon the adaptation method used.

In the cell-based embodiment, each element of the lookup table T(n)stores a numeric value corresponding to a particular cell. FIG. 5 showsan example of a two-dimensional table 140 of cells 142 (as defined bythe breakpoints 94). In the cell-based adaptation scheme, each cell 142has an adaptation weight, which depends on the specific adaptationalgorithm used. If the current operating point (x₁, x₂) lies within acell, that cell is adapted using the corresponding plant output data “d”66. The particular cell is located by comparing the input data with thebreakpoints 94 of the corresponding indexing variables. In the exampleshown, a pair of input data (x₁=2400, x₂=47) is used to locate thecorresponding cell to be updated. The adapted cell value “y” 76 and thecell number 78, that is, the values of 1.15 and 7, respectively, are theoutputs of the lookup table. The cell value can be used for control,whereas the cell number can be used as an indicator of the currentoperating point for the user or other logic. Various adaptationalgorithms used to update the cell value are discussed below.

One type of adaptation algorithm that can be employed in a cell-basedembodiment is Recursive Sample Mean (RSM). For the cell-basedembodiment, the sample mean is defined as

$\begin{matrix}{{{y(n)} = {{1/n}{\sum\limits_{i = 1}^{n}\;{d(i)}}}},} & (11)\end{matrix}$and provides the average value of n output data samples, where each d(i)is the i^(th) measurement collected within a particular cell. For eachinput data pair (x₁, x₂), the sample mean at the corresponding operatingpoint (cell) is updated using the output data measurement, d.

In practice, instead of accumulating n samples of data for each cell, arecursive relation is used to calculate the sample mean. A recursiveexpression can be obtained from the definition (11) as follows:

$\begin{matrix}\begin{matrix}{{y(n)} = {1/{n\left\lbrack {{\sum\limits_{i = 1}^{n - 1}\;{d(i)}} + {d(n)}} \right\rbrack}}} \\{= {{\left( {n - 1} \right)/{n\left\lbrack {{1/n} - {1{\sum\limits_{i = 1}^{n - 1}\;{d(i)}}}} \right\rbrack}} + {\left( {1/n} \right)*{d(n)}}}} \\{= {{\left( {n - 1} \right)/{n\left\lbrack {y\left( {n - 1} \right)} \right\rbrack}} + {\left( {1/n} \right)*{d(n)}}}}\end{matrix} & (12)\end{matrix}$where d(n) is the n^(th) data sample.

Using an estimation error defined as e(n)=d(n)−y(n−1), the recursiverelation (12) can be written asy(n)=y(n−1)+(1/n)*e(n),  (13)where n>=1 and the initial estimate y(0) is arbitrary. In thisexpression, only the number of samples, n, for each cell has to bestored in memory, instead of storing n data samples required in Equation(11). A further simplification is possible by reformulating therecursion (13) asw(n)=w(n−1)+1,y(n)=y(n−1)+e(n)/w(n),  (14)where w(n) is the recursive adaptation weight with initial value w(0)=0.

The recursive mean algorithm defined in Equation (13) has an infinitememory so that the past data samples have the same weight as the finalsample in the calculation of the sample mean. In contrast, an RSMalgorithm with a forgetting factor puts more weight on the more recentsamples and has robustness against initial response transients of theplant behavior. In addition, the forgetting factor provides anadjustable speed of adaptation. The recursive sample mean withforgetting factor is defined as

$\begin{matrix}\begin{matrix}{{y(n)} = {{1/\left\lbrack {\sum\limits_{i = 1}^{n}\;\lambda^{n - i}} \right\rbrack}{\sum\limits_{i = 1}^{n}\;{\lambda^{n - i}{d(i)}}}}} \\{= {1/{\left\lbrack {\sum\limits_{i = 1}^{n}\;\lambda^{n - i}} \right\rbrack\left\lbrack {{\sum\limits_{i = 1}^{n - 1}\;{\lambda^{n - i}{d(i)}}} + {d(n)}} \right\rbrack}}} \\{= {{\left\lbrack {{s\left( {n - 1} \right)}/{s(n)}} \right\rbrack*{y\left( {n - 1} \right)}} + {{1/{s(n)}}*{d(n)}}}}\end{matrix} & (15)\end{matrix}$

whereλε[0,1]

is the forgetting factor and

${s(k)} = {\sum\limits_{i = 1}^{k}\;{\lambda^{n - i}.}}$Using the estimation error defined as e(n)=d(n)−y(n−1), the recursiverelation (15) can be written as

$\begin{matrix}\begin{matrix}{{y(n)} = {{y\left( {n - 1} \right)} + {\left\lbrack {1/{s(n)}} \right\rbrack*{e(n)}}}} \\{{= {{y\left( {n - 1} \right)} + {\left\lbrack {\left( {1 - \lambda} \right)/\left( {1 - \lambda^{n}} \right)} \right\rbrack*{e(n)}}}},}\end{matrix} & (16)\end{matrix}$where n>=1 and the initial estimate y(0) is arbitrary. It should benoted that a small value for λ results in faster adaptation. A furthersimplification is possible by reformulating the recursion (16) asw(n)=λw(n−1)+1,y(n)=y(n−1)+e(n)/w(n)  (17)where w(n) is the recursive adaptation weight with initial value w(0)=0.

The Recursive Sample Mean and the Recursive Sample Mean with ForgettingFactor adaptation techniques discussed above are equivalent to thewell-known Recursive Least Squares (RLS) algorithm in one dimension,where the variable k(n)=1/w(n) is the gain vector.

In a point-based embodiment, each element of the lookup table stores anumeric value corresponding to a particular point which is a location inthe multi-dimensional space defined by the breakpoints of the indexingvariables. FIG. 6 shows an example of a two-dimensional point-basedlookup 150, where each dot represents a point 152. In the point-basedembodiment, each point has an adaptation weight, which depends on thespecific adaptation algorithm used. If the current operating point (x₁,x₂) lies within a cell, the points that define the boundaries of thatcell are adapted (adapted point values 134) according to where theoperating point is located relative to the measured data, shown in theexample as d=1.09. The particular cell is located by comparing the inputdata 64 with the breakpoints 94 of the corresponding indexing variables.In the example shown, a pair of input data (x₁=2400, x₂=47) 64 and theadapted points around this operating point 134 are shown in the figure.The value of the “adapted” operating point 76 (y=1.142), which is foundby interpolation of the adapted (neighboring) table points, and the cellnumber 78 are the outputs. The interpolated point table output value 76is used for control, whereas the cell number 78 is used as an indicatorof the current operating point for the user or other logic.

The adaptation algorithms used to update the point-based lookup tablevalues include, but are not limited to, the well-known Least-MeanSquares (LMS) or Recursive Least Squares (RLS) techniques. The LMStechnique uses the adaptation equations (8, 9, 10) withu(n)=u _(m)(n),m=2,  (18)where

$\begin{matrix}{{u_{i}(n)} = {{u_{i - 1}(n)} \otimes {\begin{bmatrix}{1 - {f_{i}(n)}} \\{f_{i}(n)}\end{bmatrix}.}}} & (19)\end{matrix}$In equation (19), the symbol ⊕ denotes the Kronecker product with i>=1and u₀(n)=1.

The granularity of the breakpoints sets can be used to control theprecision of the output y(n). Greater spacing between breakpointsresults in a higher degree of datapoint compression, that is, in fewercells. A reduced spacing between the breakpoints means more cells for afiner (more precise) representation of the plant output (surface).

It is also possible to incorporate into the block functionality logicthat samples the plant output data values as they are made available foruse by the adaptive lookup block 38, thus selecting which of the valuesare used (or are not used) in the adaptation.

FIGS. 7A and 7B are plant surface plots of volumetric efficiency as afunction of intake manifold pressure and engine speed. The plot shown inFIG. 7A was generated directly from measured values of volumetricefficiency, whereas the plot of FIG. 7B was generated from the output ofthe block 38 in a cell-based embodiment, that is, using adapted valuesof volumetric efficiency to provide a close approximation of the plantsurface, as seen in the figures.

The lookup table generation and adaptation block is useful in a numberof different types of applications. As already described above anddepicted in FIG. 1, the block can be used to model the steady-statebehavior of an unknown system (plant) by measuring outputs from sensorson the plant and capturing the data into the adaptive table. Thisbehavior information can then be used to construct a time-varying plantmodel that will later be used during control design. The adaptive lookuptable can also be used in a real-time environment, where sometime-varying properties of a system need to be captured. For such anapplication, the model 62 can be created and initialized using the blockdialog 90, as discussed above. Instead of executing the model during asimulation run, using measured or simulated plant data, however, themodule 24 generates executable C code from the method(s) and blockparameter values defined for the block 38 using the code generator 48,e.g., Real-Time Workshops® available from The Mathworks, Inc. The codecould then be loaded into the microcomputer or controller of the targetapplication. Applications that could use the generated adaptive lookuptable program include: real-time adaptation and control applications,e.g., of hydraulic servo or proportional valves in the presence of valvewear and pressure/flow variations, as well as control applications whichuse real-time (or off-line) generation of tables, e.g., in theautomotive context, generation of fuel tables to comply with emissionstandards and ensure that a stoichiometric Air-to-Fuel Ratio is held inthe presence of engine changes due to aging and environmentalconditions, or, in the Aerospace context, generation and adaptation offlight-tables in airplane control applications.

In some real-time adaptation and control environments in which outputdata is collected via sensors, the output data signals may beparticularly noisy. In a noisy environment, the table can be operated inadaptation mode to smooth the values in the table. That is, althoughreal output data measurements are available, it may desirable to use theprocessed lookup table values in place of those measurements. Moreover,system reliability may be enhanced through the inclusion of the lookuptable in an environment in which sensor data is normally used. Forexample, if a sensor fails, the table lookup adaptation can be disabledand the content of the table can be made available in a static tablelookup mode. Consequently, output data values are always available.

For a control application in which sensor data is not collected inreal-time, lookup table content can be captured in a laboratory firstand then loaded into a table for use in a static table lookup mode. Atsome later point in time, after the table has been operating as a staticlookup table, because system conditions may have changed over time, itmay be desirable to calibrate the table contents. Thus, the table can beconnected to sensors and switched to adaptation mode for some period oftime to calibrate the contents. Once the content has been calibrated,the table adaptation is again disabled and the table operates in statictable lookup mode with the new values generated during thecalibration/adaptation process.

It is to be understood that while the invention has been described inconjunction with the detailed description thereof, the foregoingdescription is intended to illustrate and not limit the scope of theinvention, which is defined by the scope of the appended claims. Otherembodiments are within the scope of the following claims.

1. A system comprising: a memory to store data defining a graphicalblock diagram model including an executable graphical block, thegraphical block including one or more inputs for receiving input data,the executable graphical block defining a lookup table adaptationalgorithm, the executable graphical block generating an adaptive lookuptable for simulating a plant, the lookup table adaptation algorithmadapting the adaptive lookup table when the plant is simulated, andwhere the input data received at the one or more inputs includes: firstdata that is input to the plant, and second data that is output from theplant; and one or more processors to: receive breakpoint data; partitionthe adaptive lookup table into cells based on the breakpoint data;initialize the adaptive lookup table with initial table data; generatecode to simulate the graphical block diagram model, the generated codeincluding code to simulate the adaptive lookup table; execute thegenerated code; and update data stored in the adaptive lookup tablebased on the input data received at the one or more inputs duringexecution of the generated code, the update resulting in adaption of theadaptive lookup table.
 2. The system of claim 1, where the graphicalblock includes one or more graphical block inputs that are coupled toone or more other graphical blocks in the graphical block diagram model,the one or more graphical block inputs being associated with the one ormore inputs for receiving input data.
 3. The system of claim 2, wherethe one or more processors are further configured to receive a signalassociated with the one or more graphical block inputs to disableupdating data stored in the adaptive lookup table.
 4. The system ofclaim 2, where the graphical block includes a graphical block outputthat is coupled to another graphical block in the graphical blockdiagram model.
 5. The system of claim 4, where the graphical blockoutput is associated with an index number corresponding to a location inthe adaptive lookup table having updated data.
 6. The system of claim 4,where the graphical block output is associated with an updated lookuptable.
 7. The system of claim 1, where the data input to the plant orthe data output from the plant includes measured data.
 8. The system ofclaim 7, where the data input to the plant and the data output from theplant includes real-time data.
 9. The system of claim 7, where the datainput from the plant and the data output from the plant includenon-real-time data received from a storage device.
 10. Acomputer-implemented method comprising: providing an executablegraphical block in a graphical block diagram model, where the executablegraphical block includes one or more inputs for receiving input data,and the executable graphical block defines a lookup table adaptationalgorithm, the executable graphical block generating an adaptive lookuptable, the lookup table adaptation algorithm adapting the adaptivelookup table during a simulation, where the input data received at theone or more inputs includes: first data that is input to a plant, andsecond data that is output from the plant; initializing the adaptivelookup table with initial table data; generating code to simulate thegraphical block diagram model, the generated code including code tosimulate the adaptive lookup table; executing the generated code; andupdating data stored in the adaptive lookup table based on the inputdata received at the one or more inputs during execution of thegenerated code, the updating resulting in adaption of the adaptivelookup table.
 11. The computer-implemented method of claim 10, furthercomprising simulating an embedded control system.
 12. Thecomputer-implemented method of claim 10, where the executable graphicalblock includes one or more graphical block inputs coupled to one or moreother graphical blocks, where the one or more graphical block inputs areassociated with the one or more inputs for receiving input data.
 13. Thecomputer-implemented method of claim 12, where the executable graphicalblock includes a graphical block output coupled to another executablegraphical block, the method further comprising simulating outputted dataassociated with the executable graphical block output during thesimulation.
 14. A non-transitory computer-readable medium includinginstructions executable by at least one processor, the computer-readablemedium comprising: one or more instructions for receiving, in a staticoperating mode, one or more input values for storing in an adaptivelookup table generated by an executable graphical block in a graphicalmodel, the executable graphical block defining an adaptation algorithmfor adapting the adaptive lookup table, and the executable graphicalblock executing when the graphical model is simulated; one or moreinstructions for determining at least one previously stored valuecorresponding to the input values, and producing output data using theat least one previously stored value; one or more instructions forreceiving, in a dynamic operating mode, the one or more input values andat least one additional value from a sensor, and modifying thepreviously stored at least one value corresponding to the at least oneinput value based on the at least one additional value during simulationof the graphical model; and one or more instructions for determiningwhether the sensor has failed and allowing for operation only in thestatic operating mode when the sensor has failed.
 15. An apparatuscomprising: means for providing an executable graphical block in anexecutable graphical block diagram model of a plant, where theexecutable graphical block includes inputs for receiving input data, theexecutable graphical block generates an adaptive lookup table thatincludes adaptation means, where the input data received at the one ormore inputs includes: first data that is input to the plant, and seconddata that is output from the plant; means for initializing the adaptivelookup table with breakpoint data and initial table data; means forgenerating code to simulate the executable graphical block diagrammodel; means for executing the generated code; and means for updatingdata stored in the adaptive lookup table based on the received inputdata during execution of the generated code.